Assuming she was a harlot and not, as some suggest, an innkeeper, what exactly does this mean? Did she convert? Did her conversion remove the stain of being a harlot from her (presumably because she is a new person)? Would she not be liable for punishment for her past sins? Would she have been able to marry any non-Kohen (a Kohen is prohibited from marrying any convert)?

Note that I assume most of this question can be answered with a simple "yes", any convert can be fully integrated into Klal Yisrael, including marrying any non-Kohen, even known prostitutes. But I am asking mostly for certainty about a)that assumption and b)whether she in fact converted.

2 Answers
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The Gemara at Megillah 14b says that she converted, married Joshua, and that eight prophets who were also kohanim descended from her: Neriyah, Baruch, Serayah, Machsiyah, Yirmeyahu, Chilkiyah, Chanma'el and Shalom. According to the Gemara, Rachav and Joshua had no sons, but they did have daughters.

Given that history alone, the stain of her pre-conversion life was certainly erased. But it would be anyway. At Yevamos 48b, Rabbi Yossi is quoted as holding that a convert is like a new born baby and not held liable for his previous sins.

@DoubleAA: See Yevamos 48b. Rabbi Yossi's comment is part of a discussion about why converts suffer. Rabbi Yossi rebuts the Beraisa where Rabbi Channinah states that converts suffer because they didn't observe the seven mitzvahs b'nai Noach before they converted. R. Yossi says that converts are like newborn children (and therefore aren't punished for past sins), rather they suffer for failing to be meticulous in observing mitzvahs as a Jew. In the link you offer, SimchasTorah missed R. Yossi's rebuttal, hence he mis-cited that Gemara.
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Bruce JamesJan 22 '13 at 18:31

Presumably, Rachav repented before she converted. Perhaps this is supported by the Sifrei (on Parshas D'varim 1:24, § 22), which states that Rachav possessed ruach hakodesh at the time of the spies' visit to her home. Sincere repentance can effect major improvements in one's spiritual state in a very short period of time (Rambam, Hil. Teshuvah 7:7).

Additionally, as mentioned in Bruce's answer, it is R' Yosi's opinion that conversion absolves the convert of heavenly punishment for past sins (see Yevamos 48b; Tos. Yeshanim, ad loc.) According to the gemara, Yehoshua married Rachav, which suggests that she was allowed to marry any non-Kohein (Megillah 14b).